The School of Optometry and Vision Science, University of New South Wales, Kensington, New South Wales, Australia

Michael Kalloniatis

The School of Optometry and Vision Science, University of New South Wales, Kensington, New South Wales, Australia Centre for Eye Health, University of New South Wales, Kensington, New South Wales, Australia

Correspondence: Michael Kalloniatis, Centre for Eye Health, University of New South Wales, Kensington, NSW, Australia; m.kalloniatis@unsw.edu.au.

Purpose.:
To establish Ricco's critical area (Ac) using the 30-2 Humphrey visual field analyzer (HVFA) and thereby identify Goldmann test sizes that are within or outside complete spatial summation at all visual field testing locations. We also determined the suitability of using age normative data for different test sizes. Finally, by modifying current output measures (dB values), we provide a new method that allows comparison of contrast sensitivity when testing with different Goldmann test sizes within complete spatial summation.

Methods.:
We used the HVFA in full threshold mode and measured thresholds for all five Goldmann test sizes in 12 observers. Normative data of Heijl et al. were used for age transformation and comparison.

Results.:
All the data converted to a 50-year-old equivalent lie within 1 SD of expected variance for all test locations of the 30-2 paradigm. We established Ac values at all locations of the 30-2 paradigm and showed a systematic increase in Ac as a function of increased visual field eccentricity, consistent with previous studies. Age does not appear to affect Ac or the slope of partial summation for a wide range of visual field eccentricities tested using the HVFA. By equating spatial summation, we propose a new metric, dB*, that returns a uniform sensitivity value for different test sizes that are operating within complete spatial summation (i.e., follow Ricco's law).

Conclusions.:
We established that converting to age-equivalent thresholds and application of dB* principle advantageously allows comparison of data sets across age and test size at different locations of the visual field. By identifying the Ac across the visual field, it is now possible to systematically determine threshold changes across the 30-2 locations in ocular disease and further characterize the importance of testing within complete spatial summation in standard automated perimetry.

White-on-white standard automated perimetry (SAP) is a common method used to assess visual function by quantifying the ability of the observer to perceive (i.e., the minimum contrast required to detect the stimulus) a spot of light of a standard size (Goldmann III) briefly presented (∼100–200 ms) to multiple locations across the visual field.1–4 As contrast detection is measured at discrete spatial points in the visual field, this method provides a useful measure of visual function and performance that is location specific. Accordingly, the employment of SAP is commonplace in clinical assessment and remains a gold standard for the clinical testing of visual function in the normal and abnormal visual system.3–5 In eye disease, SAP is commonly employed to map out local and global patterns of visual field loss associated with underlying structural loss in the retina. For example, visual field testing is used to detect, diagnose and monitor glaucomatous loss in peripheral vision associated with retinal ganglion cell loss.6–8

Despite the common use of SAP in vision screening and as a means of detecting eye disease, previous studies have raised questions regarding its effectiveness and sensitivity in detecting corresponding structural loss. Numerous studies have noted the rather poor “structure–function” concordance.6,9–12 It may be that the structure–function relationship requires customization to individual patients.13 However, current visual field applications may lack sufficient sensitivity to identify glaucoma compared with other methods such as optic nerve head assessment.14,15 The discrepancy between SAP and structural measures of vision has led to the proposition of the “hockey stick” model that highlights structure–function concordance and discordance depending upon the visual field location.12,16 This dependence on visual field location may reflect alterations in spatial summation characteristics in the visual psychophysical data (Kalloniatis M, et al. IOVS 2014;55:ARVO E-Abstract 3534 and Refs. 2, 17–19). Importantly, the lack of good concordance is a limitation to the effective diagnosis of eye disease and understanding its development and progress.

Ricco's law20 states that the product of the detection threshold (ΔL) and stimulus area (A) is a constant (cA = ΔL × Ak). The exponent depicts various levels of summation, from complete summation (Ricco's law: k = 1) to—for example—partial summation (Piper's law: k = 0.5) or no summation (k = 0). The transformation of the equation into log units leads to the following: log ΔL = −k × log A + log cA) and, thus, when plotting log threshold against log area, the exponent (k) indicating Ricco's law is identified as the region with a slope of −1 (e.g., the Goldmann I and II targets in Supplementary Fig. S1A that depicts spatial summation at a superonasal location of 12.7°). Deviation from −1 reflects the location of the critical area (Ac) of complete spatial summation beyond which partial summation occurs (e.g., Goldmann targets III, IV, and V in Supplementary Fig. S1A). A number of studies have proposed that a limitation in current visual field technologies relates to the size of the stimulus used (i.e., whether the stimulus is within, at, or outside Ac; Kalloniatis M, et al. IOVS 2014;55:ARVO E-Abstract 3534 and Refs. 2, 18).

In SAP, a Goldmann size III test stimulus is used to measure contrast sensitivity across the visual field. The use of a single test size across the visual field does not take into consideration the extensively documented observation that spatial summation increases with increased visual field eccentricity.19,21–23 The critical area increase with visual field eccentricity suggests greater spatial summation at peripheral rather than foveal locations.19,21,23,24 Also, Ac increases as a function of background adaptation,25,26 but does not appear to vary with age when measured psychophysically.27

Critical area increases with visual field location and is largely unexplored under SAP conditions. The use of one test size (Goldmann III) throughout the visual field in SAP1,18,19,21,26 implies that contrast sensitivity could be assessed using a stimulus that is within or outside complete spatial summation at different visual field locations. Sloan19 attributed altered spatial summation as the reason contrast sensitivity varied with stimulus size. In particular, contrast detection performance with large test sizes (Goldmann IV & V) were not greatly dependent on visual field eccentricity, while detection performance with smaller targets (Goldmann I & II), markedly decreased with visual field eccentricity.

The independence of contrast detection performance on the target size and visual field eccentricity likely limits the effectiveness of current visual field technologies as sensitivity to the target is not appropriately equated across the visual field.2,18,26 This poses a problem with early disease detection within the central 20 to 30° visual field (Kalloniatis M, et al. IOVS 2014;55:ARVO E-Abstract 3534 and Refs. 2, 18), particularly if the contribution of underlying detectors is different when the stimulus is within or outside Ac.28 If the standard size III target is larger than Ac, threshold elevation will be different to that expected when the stimulus is within Ac (where threshold changes linearly with stimulus size),28 and may display a smaller change despite loss of underlying detectors. Therefore, the contribution of normal detectors outside or on the edge of the affected region might mask early sensitivity loss due to ocular disease if large stimuli are used.6,18

Dubois-Poulsen et al.29 reported that when using kinetic perimetry, “equivalent stimuli” in glaucoma patients provided more pronounced visual field deficits not immediately obvious when using larger/brighter stimuli. The discrepancy where isopter contours were not followed led to the introduction of the term of “photometric dysharmony” (see Ref. 21 for discussion). The findings of photometric dysharmony in visual fields have been subsequently investigated in three classic studies by Sloan,19 Sloan and Brown,21 and Wilson,30 who mapped the extent of spatial summation in the periphery and in ocular disease. These studies partially mapped Ricco's area, but more importantly, found many patients displayed a larger deficit when using smaller stimuli (targets within Ricco's law), compared to the use of larger test stimuli. This finding can be attributed to the fact that larger Ac are observed in ocular disease, and this was confirmed in a large glaucoma cohort.18

Despite the importance of spatial summation in identifying the size of visual field loss in ocular disease, there is paucity in knowledge and clinical data characterizing how the Ac might change within the test field of SAP. While previous studies have attempted to characterize the Ac change with visual field eccentricity, they have typically done so along one spatial meridian (usually along the cardinal horizontal or vertical directions), or only at a particular visual field eccentricity.19,21,23,26,27,31

Our first aim was to characterize the Ac change throughout the 30-2 paradigm of the HVFA and provide a comprehensive understanding of the effect of stimulus test size on visual field testing in SAP. This information is useful for new testing protocols that seek to scale the test stimulus size relative to the Ac, as has been proposed by a number of studies (Kalloniatis M, et al. IOVS 2014;55:ARVO E-Abstract 3534 and Refs. 2, 18, 22, 26). Our second aim was to investigate the use of age correction of dB values available for all the 30-2 locations when using the Goldmann III test size.1 Our data showed that the Ac and the slope of partial summation curve does not vary with age when using the HVFA 30-2 paradigm. Assuming that both Ac and partial summation do not change with age, we developed a new metric (dB* equating stimulus area and spatial summation) that allows for the comparison of data sets for all Goldmann test sizes. Age-equivalent data values using the dB* principle is useful to equate sensitivity values for larger test sizes (greater than Goldmann III), as their use has been proposed for patients with moderate/advanced ocular disease (Gardiner SK, et al. IOVS 2013;54:ARVO E-Abstract 2636 and Refs. 32–34).

Methods

Observers

Twelve psychophysically experienced observers (age: 20–54 years; mean: 33; median: 28, SD: 11 years) participated in the present study. They had normal or corrected to normal (20/20 or better) visual acuity and had no history of any visual abnormalities beyond small refractive errors. Five subjects had refractive errors within ±0.5 diopters spheres (DS), one was a +1.50 DS hypermetrope and the remaining six had refractive errors from −1.00 to −4.5 DS (equivalent sphere). All had undergone a comprehensive eye examination including ocular imaging at the Centre for Eye Health (CFEH, at the University of New South Wales) which established no evidence of ocular disease or anomalies that would affect visual field results. A comprehensive eye examination included fundoscopic examination of the optic nerve head, posterior pole and peripheral retina, optical coherence tomography (both macular cube and optic nerve head analysis), regular and wide field fundus photography. Ethics approval was given by the relevant University of New South Wales Ethics committee and the observers gave informed consent prior to data collection with the research following the tenets of the Declaration of Helsinki.

Apparatus and Procedures

We used the HVFA to measure contrast sensitivity at 75 spatial locations in accordance with the 30-2 testing protocol using the full threshold paradigm. We maintained the full threshold paradigm as different thresholding paradigms result in altered threshold levels.35 Thresholds were measured at least twice for each observer, and these values were averaged to provide an estimate of the contrast threshold at each location. The short-term fluctuation option was enabled and thus some locations had more than two thresholds. This process was repeated for the five different test sizes available on the HVFA (Goldmann targets I–V). Testing was performed with one eye (other eye was patched) with natural pupils and the order in which observers were tested with the different test sizes was randomized to minimize any order effects. For clarity, all data were converted to right eye orientation. Refractive correction was provided in the HVFA trial frame as calculated by the HVFA algorithm. Sufficient breaks were given between tests to avoid fatigue with testing occurring over three to four sessions.

In ocular disease, the higher threshold elevation for a stimulus smaller than the area of complete spatial summation compared with thresholds in the area of partial summation, has led to proposals to scale test stimuli to the Ac to maximize detection of eye disease.2,18,26 There are two confounding issues to be overcome before implementing such a proposal. First, in order to scale test size for a specific Ac at different locations of SAP, the Ac has to be established at all the visual field locations. The second issue surrounds the use of different test sizes at different eccentricities. The use of the current dB scale will lead to higher dB values for smaller stimuli in order for an equivalent number of quanta to be delivered for other test sizes (see Goldmann I and II thresholds in Supplementary Fig. S1A). For example, if we assume that Goldmann targets I, II, and III are all within complete spatial summation in the far periphery of Figures 1 and 2A through 2D, the dB value is clearly dependent on the spatial size of the stimulus with different sizes returning different sensitivity values. Importantly, the dependency of contrast sensitivity (using current dB values) on stimulus size, does not immediately allow for direct comparisons between different test sizes. This is because the influence of test size on thresholds has not been discounted. To address this limitation, we introduce a new dB value—defined as dB*—which serves to equate the contrast sensitivity value with the degree of spatial summation associated with a particular test size.

The value of dB* is based upon Ricco's law of spatial summation that states the threshold × area = constant. In log units, dB* = dB (as per normal visual field output) + a size factor (in dB). The absolute value of the size factor is not important but rather its product (or sum if both values are in log units). In the conversion of dB*, we have chosen to use the Goldmann size III as the constant value, and the size factor (expressed in dB value) for the different Goldmann sizes were: size I (+12); size II (+6); size III (0); size IV (−6); and size V (−12). The 6-dB change for different test sizes reflects the 0.6 log unit difference for each Goldmann test size area.

As the sum of the logarithm of two values is the logarithm of the product of those values, the dB* conversion is equivalent to expressing data as log (ΔL × A) versus log A, where ΔL is the luminance threshold and A is the area of the stimulus. Thus, Ricco's law accords with a slope of 0 (such that ΔL × A = cA where cA is a constant24,36–39). Importantly, this application means that the dB* value is equated for spatial summation within Ricco's area (complete spatial summation) and is the same dB* value irrespective of test size for stimuli within Ricco's area. This advantageously enables comparison of thresholds within Ricco's law irrespective of test size. Outside this area, the slope will increase by a different value (e.g., 0.5 for Piper's region) and up to a slope of 1 (no spatial summation). Additionally, using the dB* value, the established decibel values are maintained when using a size III target (done for ease of conversion).

Using dB Values and Luminance/Contrast Conversion: Comparison With Published Normative Data

Standard automated perimetry expresses sensitivity values as a decibel, which is an attenuation measure of the maximum possible test spot luminance. Although the use of the dB value to express threshold or sensitivity is not a correct use of terminology, the dB nomenclature is well established and thus our analysis continues to use this nomenclature. In this study, we use the terms contrast sensitivity and depict this using dB or our newly defined dB* value. The correct contrast sensitivity value can be derived using the simple conversion equations that allow the conversion of a HVFA dB value to threshold luminance ΔL in cd/m2 or threshold contrast ΔL/L given the maximum luminance of the test spot at 3183 cd/m2 and the luminance of the background (L) of 10 cd/m2. The new definition of dB* modifies the dB value using a test size conversion (defined earlier), and by converting back to dB value, Equation 1 or 2 can be used to derive luminance or contrast.

All subject data sets were converted to a 50-year-old equivalent using the Heijl et al.1 age per decade data (fig. 2 in Heijl et al.1) at each of the 30-2 locations, and compared with the dB sensitivity profile therein (fig. 5 in Heijl et al.1). This method of adjusting dB values relative to age has been used in a previous study40 as an effective means of discounting the effect of age on contrast sensitivity and thereby standardizing their data.

Fitting Paradigm and Statistical Analysis

We derived an estimate of the Ac value at each location within the 30-2 paradigm by converting the data expressed in dB values to dB*, and at each point, the dB* values were considered as a function of test stimulus size (in log area in degrees2). Two-line segmental linear regression was fitted to these data using a least squares approach in a graphing and statistics environment (GraphPad Prism version 6; GraphPad Software, Inc., La Jolla, CA, USA) to determine the inflection point, which provided an estimate of the Ac. This fit fixed the slope of the first line to 0 (representing complete spatial summation within Ricco's area); but the slope of the second line was free to vary to reflect partial or no spatial summation. Accordingly, the Ac point provides an indication of the stimulus size at which thresholds no longer are governed by complete summation.

We also tested the hypothesis that Ac does not change with age at eccentricities outside the 10° examined by Redmond et al.27 Using non–age-corrected contrast threshold data for our subjects, we determined the Ac values (as described above) for individual participants for a number of test locations on the 30-2 test grid. For each of these locations, a linear regression analysis (using graphing software [GraphPad Software, Inc.]) derived the line that associated Ac with age. We assumed no significant (α = 0.05) interaction if the slope of the fitted line did not deviate from zero.

We also investigated whether partial summation changes with age. As with our analysis of Ac and age, non–age-corrected contrast thresholds were first fitted with a two-line functions (as described above), and the slope of the second line, which provided an indication of partial summation, was estimated. This analysis was performed for all 75 points in the 30-2 paradigm. For each location, linear regression analysis provided an indication of the relationship between the extent of partial summation and age. For comparison, we also examined the effect of age on partial summation using the achromatic dataset for superior and inferior visual field locations from Redmond et al.27 at 10°. Redmond et al.27 had a larger sample size of participants than the present study with the observers clustered into five age groups (20–29, 30–39, 40–49, 50–59, and >60 years), and the spatial summation curves derived for each observer within these groups were averaged (fig. 2 in Redmond et al.27). We used data point extraction software (DataThief41; http://datathief.org, in the public domain) to extract these data and a two-line fit were performed (per procedures discussed above) to estimate the spatial summation curve and the slope of the second line, which provided an indication of the degree of partial summation for each age group examined by Redmond et al.27 For these analyses we assumed no significant (α = 0.05) interaction if the slope of the fitted line did not deviate from zero.

Data were analyzed using a two-way ANOVA also conducted using commercial software (GraphPad Software, Inc.). A Kolmogorov-Smirnov normality test (with Dallal-Wilkinson-Lillie for an α = 0.01) confirmed that the observer data (dB values) were normally distributed for all points and across the five test sizes.

Comparing Data From Previously Published Work

Published data were collected using the point extraction software Datathief41 and fitted as per the ‘hockey-stick' model of Swanson et al.16 An inflection point at ∼15° eccentricity is regarded at the location where structure-function departs from a 1:1 relationship and reflects approximately 31 ganglion cells within a Goldmann III target.16,40,42 We compared our data set with an example of an equivalent visual field location40 (Supplementary Fig. S1A), and assessed the error associated for the predicted 15° eccentricity where structure/function concordance is thought to fail (see Supplementary Material for details).

Results

Normative dB Values for Goldmann Tests I Through V Across the Visual Field

Figure 1 shows the dB ± SD for the spatial locations (grids) of the 30-2 paradigm for Goldmann test sizes I through V (in dB) in separate panels. The data represented the average of the 12 observers. Before averaging, individual data were converted to a 50-year-old equivalent using the dB change per decade for each 30-2 location provided by Heijl et al.1 As mentioned, this conversion was performed because age has been shown to be an important factor in visual field detection performance, and allowed for standardization of thresholds between observers of different ages and comparison with the established data provided by Heijl et al.1

A plot of mean dB ± SD contrast sensitivity values (n = 12 subjects) for points in the HVFA 30-2 paradigm for Goldmann sizes I through V. Thresholds for Goldmann III for each subject were age-corrected and then averaged. The averaged data were then compared with those of Heijl et al.1 (middle right panel) showing the dB differences between the two. Age correction was also applied to sizes I, II, IV, and V. Error values represent 1 SD.

Figure 1

A plot of mean dB ± SD contrast sensitivity values (n = 12 subjects) for points in the HVFA 30-2 paradigm for Goldmann sizes I through V. Thresholds for Goldmann III for each subject were age-corrected and then averaged. The averaged data were then compared with those of Heijl et al.1 (middle right panel) showing the dB differences between the two. Age correction was also applied to sizes I, II, IV, and V. Error values represent 1 SD.

Contrast sensitivity (in dB) from locations in the 30-2 paradigm plotted as a function of visual field eccentricity along four different axes (A–D). All the data reflect sensitivities after correction to the 50-year-old equivalent. The schematic diagram associated with each plot indicates the orientation axis. Note that for the 0 through 180° (A) and 90 through 270° axes (B), the fovea (at 0°) data is not continuous with the points at other eccentricities which were 3° about the vertical or horizontal axes. (C, D) Oblique axes. Error bars signify 95% confidence limits.

Figure 2

Contrast sensitivity (in dB) from locations in the 30-2 paradigm plotted as a function of visual field eccentricity along four different axes (A–D). All the data reflect sensitivities after correction to the 50-year-old equivalent. The schematic diagram associated with each plot indicates the orientation axis. Note that for the 0 through 180° (A) and 90 through 270° axes (B), the fovea (at 0°) data is not continuous with the points at other eccentricities which were 3° about the vertical or horizontal axes. (C, D) Oblique axes. Error bars signify 95% confidence limits.

To facilitate comparison between our data and the published norms outlined by Heijl et al.1 in Figure 1 (framed plot), we provide a difference plot that directly compared our data for the detection of a Goldmann III target (at all 75 points) with the 50-year-old data set published by Heijl et al.1—who converted their individual subject data (age range, 20–80 years) for each location to a 50-year-old equivalent using their pointwise dB per decade conversion. The framed plot in Figure 3 shows that our results are similar to Heijl et al.,1 with the average mean difference of −0.01 dB and a standard deviation of 0.665 dB. There are only two values in grids (the position inferior-temporal to the fovea and the foveal location) where the mean dB of the Heijl et al.1 data was greater than 1 SD from our age-corrected data. Conversely, the difference between our 12 subjects and the data of Heijl et al.1 can be assessed against the standard deviation value of the interindividual deviation (fig. 6 of Heijl et al.1). Only the foveal value is outside 1 SD, and thus we conclude that the conversion of dB threshold data to a 50-year-old equivalent obtained using the full threshold paradigm is a suitable mechanism to compare data across age groups.

Representative spatial summation plots depicting contrast senstivity change (as dB*) against the size of the test stimulus for three visual field locations. The 30-2 map contains the Ac values and 1 standard error of the mean for the 75 locations. The locations of the three spatial summation plots are highlighted as corresponding levels of gray on the 30-2 map.

Figure 3

Representative spatial summation plots depicting contrast senstivity change (as dB*) against the size of the test stimulus for three visual field locations. The 30-2 map contains the Ac values and 1 standard error of the mean for the 75 locations. The locations of the three spatial summation plots are highlighted as corresponding levels of gray on the 30-2 map.

Area of critical summation for different retinal eccentricities along different axes of the 30-2 paradigm. Error bars represent 95% confidence intervals. For reference, horizontal lines indicate Goldmann test sizes I through III.

Figure 4

Area of critical summation for different retinal eccentricities along different axes of the 30-2 paradigm. Error bars represent 95% confidence intervals. For reference, horizontal lines indicate Goldmann test sizes I through III.

Analysis of critical area (Ac) as a function of age (A). Ac versus age for three representative visual field locations (correspond to the shaded regions in [B]). The individual data are not age-corrected. The line is a linear regression fit to the data to determine if the slope deviated from zero. (B) The 30-2 locations where the analysis was performed: the fovea; inner test targets (eccentricity of 4.24°); the subsequent ring of points (average of ∼11° eccentricity); and finally, an outer ring of points at an average visual field eccentricity of 22°. The number at each location reflects the slope of the regression line. In all the tested locations, the slope was not significantly (NS) different to zero. Error bars are 1 standard error of the mean.

Figure 5

Analysis of critical area (Ac) as a function of age (A). Ac versus age for three representative visual field locations (correspond to the shaded regions in [B]). The individual data are not age-corrected. The line is a linear regression fit to the data to determine if the slope deviated from zero. (B) The 30-2 locations where the analysis was performed: the fovea; inner test targets (eccentricity of 4.24°); the subsequent ring of points (average of ∼11° eccentricity); and finally, an outer ring of points at an average visual field eccentricity of 22°. The number at each location reflects the slope of the regression line. In all the tested locations, the slope was not significantly (NS) different to zero. Error bars are 1 standard error of the mean.

Slope of partial summation curve from Redmond et al.27 and the current HVFA results. (A) The slope of the second line representing partial summation derived from Redmond et al.27 is plotted as a function of the mid-age of five age groups, for the superior and inferior visual field locations. Data were fitted with linear functions to determine the relationship between partial summation and age as indicated by the slope of the fitted line. (B) The slope of the second, line representing linear fits to data of spatial summation from this study, is plotted for four locations (corresponding to the shaded regions in [C]). The individual data are not age corrected. (C) The slope value of the fitted line is plotted for all locations in the 30-2 HVFA paradigm. The location denoted by * indicates that the slope at this location was significantly different from 0, which indicated that partial summation changed with age. At all other locations, there was no significant difference between age and partial summation. Error bars are 1 standard error of the mean.

Figure 6

Slope of partial summation curve from Redmond et al.27 and the current HVFA results. (A) The slope of the second line representing partial summation derived from Redmond et al.27 is plotted as a function of the mid-age of five age groups, for the superior and inferior visual field locations. Data were fitted with linear functions to determine the relationship between partial summation and age as indicated by the slope of the fitted line. (B) The slope of the second, line representing linear fits to data of spatial summation from this study, is plotted for four locations (corresponding to the shaded regions in [C]). The individual data are not age corrected. (C) The slope value of the fitted line is plotted for all locations in the 30-2 HVFA paradigm. The location denoted by * indicates that the slope at this location was significantly different from 0, which indicated that partial summation changed with age. At all other locations, there was no significant difference between age and partial summation. Error bars are 1 standard error of the mean.

An informative method of gauging the effect of spatial summation on contrast sensitivity is to examine the sensitivity profile for different test sizes along various meridians of visual field space. We provide a summary plot (Figs. 2A–D) reporting the contrast sensitivity change (expressed in dB values), with increasing eccentricity for different test sizes along 4 nominal axes (horizontal, vertical, left- and right-oblique). Note that for the vertical (90–270°) and horizontal (0–180°) axes, the reported values represent the average of points (3° offset from zero) about the horizontal and vertical midlines (see schematic diagram in each plot that shows the points used to construct the figure). Note also that the foveal data are not continuous along these axes. For the two oblique axes (45–225° and 135–315°), only the last points on the curve were the average of left and right points along the axes orientation. Importantly, these summary plots provide an indication of the hill of vision (HoV) that describes the contrast sensitivity change with increasing visual field location.

In Figure 3, the three inserts display three locations from central to peripheral visual field locations highlighting the change in complete spatial summation with visual field eccentricity. In these plots, data falling along a slope of zero are within complete spatial summation with the inflection point identifying the location of Ac (the average R2 of the fits was 0.96). For the more central test point, only test size I is within complete spatial summation with the Ac value just smaller than Goldmann II. The most eccentric visual field location shows Goldmann I, II, and III test sizes within Ac, with the middle visual field location showing only Goldmann I and II within Ac (i.e., fall on the line with zero slope). The complete data set of Ac values for all the 30-2 locations for the HVFA are shown in Figure 3 (right grid).

To compare how the Ac changes with visual field eccentricity, the Ac for points along four axes (horizontal, vertical, and two oblique axes) in the 30-2 paradigms of the HVFA are plotted in Figure 4. Note that the critical areas for vertical and horizontal axes was the average of the two locations (3° offset from zero) about the horizontal or vertical axis (as in Fig. 2); therefore, they are not continuous with the foveal value. This plot demonstrates two findings. First, the Ac systematically increases with visual field eccentricity, changing by approximately 0.75 log units from the fovea to the furthest visual field eccentricity. Second, this change in Ac (within the spatial limits of the 30-2 paradigm) is approximately the same at nasal and temporal locations and along the four different axes.

We also determined if Ac varied with age at different visual field locations within the 30-2 HVFA paradigm (Fig. 5). Representative plots of the relationship (line of best fit) are shown for three locations in Figure 5A for the foveal points and eccentric locations of 9.5° and 21.2°. This data trend for multiple eccentric locations confirms that Ac does not change with age within the central ∼24° (Fig. 5B). A similar analysis of the fitted Ac value derived from Figure 2 of Redmond et al.27 also showed no significant effect with age (data not shown), confirming the original conclusion of this study.

Linear regression analysis was performed to establish whether a relationship is observed between partial summation and age (Fig. 6). We first determined the slope of the second line from the data showing contrast threshold as a function of the mid-age of each group for superior and inferior visual field locations derived from the 10° oblique orientations of Redmond et al.27 This analysis showed that for both superior and inferior locations, the slope of the second line was approximately 0.0026 and −0.0007, respectively, and they were not significantly different from 0 (P > 0.5150). This finding appears to indicate that partial summation did not change with age in the dataset reported by Redmond et al.27 Second, we provide a representative plot of the relationship between the estimated slope of the second line (which provides an indication of partial summation) and age in Figure 6B for four eccentric locations highlighted as different gray levels for the HVFA data. The slope value describing partial summation and age are given in Figure 6C for all 75 points. Our analysis showed that at 74 out of 75 points, there was no significant relationship between partial summation and age. Only one point (indicated by *) was significantly different (slope = −0.008, P = 0.0312), but this change with age is minimal.

The analysis of the data from Redmond et al.27 and our HVFA data set appears to show that partial summation is not dependent on age (over the age range of the subjects who participated in the studies). This finding applies for the vast majority of points within the 30-2 HVFA paradigm and at 10° eccentric locations examined by Redmond et al.27 (Fig. 6).

Sensitivity as a Function of Visual Field Location When Using dB*

The impact of considering sensitivity as dB* is most evident when it is used to depict the HoV. Figure 7 represents the average of superior and inferior points along the horizontal axis converted to dB* values for the 0 to 180° axis plot in Figure 2A. If test stimuli are smaller than the area of complete spatial summation, dB* values would be the same leading to overlapping values at different visual field eccentricities.

A two-way ANOVA conducted on the data depicted in Figure 7 reported a main effect of both stimulus size (F[4,550] = 629.2, P < 0.0001) and eccentricity (F[9,550] = 101.6, P < 0.0001), though a significant interaction effect was also observed (F[36,550] = 3.393, P < 0.0001), which indicated that the contrast sensitivity value was dependent on both factors. Tukey's multiple comparison tests (corrected for multiple comparisons at an α of 0.05) were conducted to compare the mean dB* values at each visual field eccentricity between different test sizes across all points. These post hoc tests indicated that the dB* values for test sizes I and II were significantly different at the fovea (P = 0.0102), but not for points beyond central vision (P > 0.05). As evident in Figure 7 at eccentric locations dB* values for test sizes I and II overlap, which indicates that these test sizes are likely to be within Ricco's area of complete spatial summation. For a Goldmann III target, the dB* value is significantly different (P < 0.01) from sizes I and II across the range of eccentricities, with the exception of the outermost points (i.e., greater than 21.7° in both nasal and temporal directions). Accordingly, a size III is outside Ricco's area for all inner points, but is inside Ricco's area for the outermost points. For sizes IV and V, at all spatial locations, these target sizes were not within Ricco's area, as their dB* values did not significantly overlap with each other or with all smaller target sizes (P < 0.001). These results confirm that dB* is a suitable measure allowing comparisons of dB* values irrespective of target size, if the target size chosen is operating within complete spatial summation.

Discussion

In this study, we determined the change in contrast sensitivity across the HVFA 30-2 visual field locations and in the Ac at all these locations, and proposed a new dB* value that corrects for differences in spatial summation for test stimuli that are within complete spatial summation. Based upon the prediction of the hockey-stick model16 of a failure of structure–function at ∼150 and the results of this study, contrast detection is likely not independent of test size at all 30-2 test locations in healthy individuals across age. Larger test sizes (e.g., sizes IV & V) display a smaller sensitivity change with visual field eccentricity compared to smaller stimuli (e.g., sizes I & II). The dependence of contrast sensitivity on stimulus size agrees with previous reports and is reliant on whether the stimulus size is within or outside Ricco's area.19,22,31

While previous studies and our data have shown that there is a degree of variability in contrast thresholds with different test sizes, we generally observe lower contrast sensitivity with smaller targets, which is a consequence of the test size being smaller than Ricco's area. A decrease in contrast detection performance arises because the stimulus size falls further within the Ac for increasing visual field eccentricities.19,22,23 Conversely, contrast sensitivity of larger targets do not generally change with eccentricity because their size remains outside the Ac and contrast detection is comparatively superior (than a smaller target). These results confirm the importance of test size with visual field location to explain the sensitivity change originally highlighted by Sloan.19 The use of the 50-year-old equivalent for different test size spectral sensitivity is based on the assumption that the slope of the second line of the bilinear function is a straight line and that the intercept of the two lines identifies Ac. Some models vary the slope gradually for data within partial summation region28; if a high enough density of data is available, threshold data around the two-line fit inflection point lie above where the bilinear lines meet (see fig. 2A in Glezer39), implying Ac values are slightly overestimated when a two-line fit is used.

The present study is informative as it characterizes the change across all points in a 30-2 paradigm using different size targets. To our knowledge, this has not been reported in the literature, and our data are useful in providing the basis for any future consideration that might modify visual field technologies by scaling the size of the stimulus to take into consideration spatial summation (Kalloniatis M, et al. IOVS 2014;55:ARVO E-Abstract 3534 and Refs. 2, 18, 19) or use larger test targets in moderate to advanced eye disease.31–34 These results apply for the background luminance of the HVFA (10 cd/m2) since Ac varies with background luminance levels.25,26 The scaling of the stimulus to a size that would lead to complete spatial summation requires a unit that provides the same value irrespective of test size. The use of the dB* unit, the transformed dB value that equates sensitivity value for test size differences, provides a useful method to assign a uniform sensitivity value irrespective of test size. The dB* definition holds when thresholds are within complete spatial summation. Clearly, in order to maximize the dynamic range of current visual field testing instruments, the largest Goldmann size within or at Ac would be used.

Correcting Sensitivity Values for Different Ages and for Different Test Target Size

Heijl et al.1 provided a dB per decade conversion for all the 30-2 locations as it is well established that contrast sensitivity varies with age and location.43–46 We demonstrated that using the age correction per decade of Heijl et al.,1 it is possible to obtain concordance for dB values across the whole of the 30-2 visual field for the Goldmann III stimulus (Fig. 1). This result and the finding that both Ac18,27 and the slope of partial summation do not appear to change with age (Figs. 5, 6), allows us to provide age-corrected data expressed in dB values for a 50-year-old equivalent for Goldmann test sizes I, II, IV, and V. With the pointwise correction of Heijl et al.,1 individual data sets can be compared or transformed to any age group for these additional Goldmann test sizes. These modifications advantageously allow comparison of data across age, test size, and eccentric location if nonstandard test sizes are used in the HVFA (Gardiner SK, et al. IOVS 2013;54:ARVO E-Abstract 2636 and Refs. 2, 18, 26, 32–34). Also, a number of studies have confirmed that in moderate to advanced ocular disease, variability improves with larger test targets (Gardiner SK, et al. IOVS 2013;54:ARVO E-Abstract 2636 and Refs. 33, 34) and that standard size III may be unreliable at ≤15 dB.32 Thus, the suggested paradigm using small stimuli within or at Ac likely maximizes vision loss detection in early disease and complements the large test field approach in advanced disease to optimally detect residual visual function. Consideration should be given to the use of test size in perimetric testing to move beyond practical engineering design47 and use clinically relevant design principles.

Spatial Summation Across the 30-2 Testing Locations

The foveal to peripheral sensitivity differences have led to a number of methods to scale visual stimuli as a function of eccentricity. These include using the cortical magnification factor48,49; scaling the visual field using changes in summation index (tangential slope at Goldmann III test size of log threshold versus log area functions)40; aligning test size with Ac at different visual field eccentricities.2,18,26,27 We provide a complete map of Ac values for points in the 30-2 paradigm, and thereby provide an indication of whether Goldmann test sizes fall within or outside complete spatial summation when using clinical perimetry. According to our data, at the fovea, a Goldmann size I is within Ricco's area (falling below the horizontal line corresponding to a size I target in Fig. 3). A Goldmann size II is within the region of spatial summation for eccentricities greater than approximately 10–15° (in nasal and temporal locations), while a Goldmann III is close to the Ac for the outer most points (27°).

Although proposals exist to scale test size to Ac and maximize threshold differences in early ocular disease,2,18,26 there is a paucity of data on the Ac and thus what scaled test size is required at different eccentricities and locations. We now provide these values for Ac at each point in the 30-2 paradigm (see Fig. 3), to complement those from a laboratory-based study.22 We find, consistent with previous reports, that the Ac increases with visual field eccentricity,22–24 and confirm that this change is uniform across different spatial meridians in both temporal and nasal directions within the spatial limits of the 30-2 paradigm. Wilson23 measured spatial summation in the nasal visual field along the horizontal meridian. Anderson2 (his fig. 2), replotted the data of Wilson23 and showed that Ac would be within spatial summation at around 40° when using a Goldmann III stimulus. However, Wilson23 used a tungsten background (212 cd/m2) and stimulus duration (130 ms) unlike those used in SAP. In view of this, it is not possible to directly compare the Ac results of Wilson23 to those found under the conditions of SAP beyond to note the Ac increase with eccentricity. Although variability in Ac estimates is evident, the more recent studies of Redmond et al.18,27 reported a log Ac (deg2) of approximately −1.3 at 10° eccentricity, similar to our findings (Fig. 4) and comparable to the data from Garway-Heath et al.40 (Supplementary Fig. S1A). We have also extended the comparison of Ac and age beyond the 10° visual field location that Redmond et al.27 measured and showed that there is no age effect for Ac (at least over the 20–54 age range) within visual field eccentricities tested by the 30-2 paradigm of the HVFA. In addition, our reanalysis of the slope of the partial summation line for the data of Redmond et al.27 and the analysis of our HVFA data indicated that partial summation does not appear to be affected by age. For the majority of points, we find no significant change in the extent of partial summation (as approximated by the slope of second line used to determine the Ac) and age. However, a limitation to consider when using data sets derived from SAP is that only five test sizes are available to determine the Ac value and the slope of the second line (reflecting partial summation).

Practical Application of Test Stimuli at or Below the Ac Using dB*

A number of studies have proposed to scale the Goldmann test size to Ac while other studies have proposed the use larger Goldmann test sizes in moderate/advanced disease.2,18,26,32–34 If sensitivity is reported using the current dB metric, the adoption of different test sizes would lead to different dB values for the same location (Supplementary Fig. S1A). In order to be able to compare sensitivity values, a new metric that equates test area is required. The dB* is scaled for test size and is identical when test stimuli are within Ricco's spatial summation. By using the largest Goldmann size that falls within or at Ac, it would be possible to measure contrast sensitivity across the visual field with stimuli that lie within total spatial summation.20 This approach should theoretically maximize the detection of eye disease (Kalloniatis M, et al. IOVS 2014;55:ARVO E-Abstract 3534 and Refs. 2, 18) and test the prediction that threshold changes are more detectable when tested within total spatial summation. Preliminary results (Kalloniatis M, et al. IOVS 2014;55:ARVO E-Abstract 3534) support this proposition.

How Are Ac Values Related to Swanson's Hockey Stick Model?

A number of models have been proposed that compare anatomical and perceptual data (reviewed by Malik et al.12). One such model relevant to our study is the hockey stick model (which relates structure–contrast sensitivity across a range of eccentricities) proposed by Swanson et al.16 This model predicts a failure of the 1:1 relationship at an eccentricity of 15° and smaller. The first step in generating a relationship between threshold (dB for size III target) and ganglion cell receptive field count for a Goldmann size III target, involved fitting log decalamberts versus log test spot retinal area to obtain a slope of the tangent defined as k or the coefficient of summation.40 This slope parameter is related to the Ac, but clearly reflects a different measure to the critical area we have determined. We have fitted the data of Swanson et al.16 and find an equivalent estimate of failure of the 1:1 relationship at 16°. We do note, however, that the error estimates are large when making such comparisons. The Supplementary Material provides details on this estimate: the error associated with the fitting process50 and limited number of samples in the data set,42 considering the length of Henle's fibers,51 and changes due to retinal shrinkage/expansion.52–54 We have conservatively estimated the error in estimating the retinal eccentricity where the 1:1 relationship fails when considering the hockey-stick model at approximately 36% (see Supplementary Material for details). Therefore, there are inherent errors when data sets are combined and their indicative use should specify such errors. Future use of in vivo anatomical data (optical coherence tomography), combined with visual thresholds that are equated for spatial summation differences, may be a mechanism to obtain useful structure–functional relationships with more refined error estimates.

Acknowledgments

We thank two anonymous reviewers for providing manuscript feedback and Cornelia Zangerl, Elizabeth Wong, and Nayuta Yoshioka for data collection and manuscript formatting.

Supported by the National Health and Medical Research Council of Australia (NHMRC #1033224) and the Australian Research Council (DP110104713). The Centre for Eye Health is an initiative between UNSW Australia and Guide Dogs NSW/ACT, which are partners on the NHMRC grant.

A plot of mean dB ± SD contrast sensitivity values (n = 12 subjects) for points in the HVFA 30-2 paradigm for Goldmann sizes I through V. Thresholds for Goldmann III for each subject were age-corrected and then averaged. The averaged data were then compared with those of Heijl et al.1 (middle right panel) showing the dB differences between the two. Age correction was also applied to sizes I, II, IV, and V. Error values represent 1 SD.

Figure 1

A plot of mean dB ± SD contrast sensitivity values (n = 12 subjects) for points in the HVFA 30-2 paradigm for Goldmann sizes I through V. Thresholds for Goldmann III for each subject were age-corrected and then averaged. The averaged data were then compared with those of Heijl et al.1 (middle right panel) showing the dB differences between the two. Age correction was also applied to sizes I, II, IV, and V. Error values represent 1 SD.

Contrast sensitivity (in dB) from locations in the 30-2 paradigm plotted as a function of visual field eccentricity along four different axes (A–D). All the data reflect sensitivities after correction to the 50-year-old equivalent. The schematic diagram associated with each plot indicates the orientation axis. Note that for the 0 through 180° (A) and 90 through 270° axes (B), the fovea (at 0°) data is not continuous with the points at other eccentricities which were 3° about the vertical or horizontal axes. (C, D) Oblique axes. Error bars signify 95% confidence limits.

Figure 2

Contrast sensitivity (in dB) from locations in the 30-2 paradigm plotted as a function of visual field eccentricity along four different axes (A–D). All the data reflect sensitivities after correction to the 50-year-old equivalent. The schematic diagram associated with each plot indicates the orientation axis. Note that for the 0 through 180° (A) and 90 through 270° axes (B), the fovea (at 0°) data is not continuous with the points at other eccentricities which were 3° about the vertical or horizontal axes. (C, D) Oblique axes. Error bars signify 95% confidence limits.

Representative spatial summation plots depicting contrast senstivity change (as dB*) against the size of the test stimulus for three visual field locations. The 30-2 map contains the Ac values and 1 standard error of the mean for the 75 locations. The locations of the three spatial summation plots are highlighted as corresponding levels of gray on the 30-2 map.

Figure 3

Representative spatial summation plots depicting contrast senstivity change (as dB*) against the size of the test stimulus for three visual field locations. The 30-2 map contains the Ac values and 1 standard error of the mean for the 75 locations. The locations of the three spatial summation plots are highlighted as corresponding levels of gray on the 30-2 map.

Area of critical summation for different retinal eccentricities along different axes of the 30-2 paradigm. Error bars represent 95% confidence intervals. For reference, horizontal lines indicate Goldmann test sizes I through III.

Figure 4

Area of critical summation for different retinal eccentricities along different axes of the 30-2 paradigm. Error bars represent 95% confidence intervals. For reference, horizontal lines indicate Goldmann test sizes I through III.

Analysis of critical area (Ac) as a function of age (A). Ac versus age for three representative visual field locations (correspond to the shaded regions in [B]). The individual data are not age-corrected. The line is a linear regression fit to the data to determine if the slope deviated from zero. (B) The 30-2 locations where the analysis was performed: the fovea; inner test targets (eccentricity of 4.24°); the subsequent ring of points (average of ∼11° eccentricity); and finally, an outer ring of points at an average visual field eccentricity of 22°. The number at each location reflects the slope of the regression line. In all the tested locations, the slope was not significantly (NS) different to zero. Error bars are 1 standard error of the mean.

Figure 5

Analysis of critical area (Ac) as a function of age (A). Ac versus age for three representative visual field locations (correspond to the shaded regions in [B]). The individual data are not age-corrected. The line is a linear regression fit to the data to determine if the slope deviated from zero. (B) The 30-2 locations where the analysis was performed: the fovea; inner test targets (eccentricity of 4.24°); the subsequent ring of points (average of ∼11° eccentricity); and finally, an outer ring of points at an average visual field eccentricity of 22°. The number at each location reflects the slope of the regression line. In all the tested locations, the slope was not significantly (NS) different to zero. Error bars are 1 standard error of the mean.

Slope of partial summation curve from Redmond et al.27 and the current HVFA results. (A) The slope of the second line representing partial summation derived from Redmond et al.27 is plotted as a function of the mid-age of five age groups, for the superior and inferior visual field locations. Data were fitted with linear functions to determine the relationship between partial summation and age as indicated by the slope of the fitted line. (B) The slope of the second, line representing linear fits to data of spatial summation from this study, is plotted for four locations (corresponding to the shaded regions in [C]). The individual data are not age corrected. (C) The slope value of the fitted line is plotted for all locations in the 30-2 HVFA paradigm. The location denoted by * indicates that the slope at this location was significantly different from 0, which indicated that partial summation changed with age. At all other locations, there was no significant difference between age and partial summation. Error bars are 1 standard error of the mean.

Figure 6

Slope of partial summation curve from Redmond et al.27 and the current HVFA results. (A) The slope of the second line representing partial summation derived from Redmond et al.27 is plotted as a function of the mid-age of five age groups, for the superior and inferior visual field locations. Data were fitted with linear functions to determine the relationship between partial summation and age as indicated by the slope of the fitted line. (B) The slope of the second, line representing linear fits to data of spatial summation from this study, is plotted for four locations (corresponding to the shaded regions in [C]). The individual data are not age corrected. (C) The slope value of the fitted line is plotted for all locations in the 30-2 HVFA paradigm. The location denoted by * indicates that the slope at this location was significantly different from 0, which indicated that partial summation changed with age. At all other locations, there was no significant difference between age and partial summation. Error bars are 1 standard error of the mean.